On Matrix Models of M5-branes

We compare the $(0,2)$ theory of the single M5 brane decoupled from gravity in the lightcone with transverse $R^4$, and a matrix model description in terms of quantum mechanics on instanton moduli space. We give some tests of the Matrix model in the case of multi fivebranes on $R^4$. We extract constraints on the operator content of the field theory of the multi-fivebrane system by analyzing the Matrix model. We also begin a study of compactifications of the $(0,2)$ theory in this framework, arguing that for large compactification scale the $(0,2)$ theory is described by super-quantum mechanics on appropriate instanton moduli spaces.